Veritas Prep 10 Year Anniversary Promo Question #5

Answer is C
1) insufficient as q can be 1 or 0
2) Insufficient
3) Q = is 1 as r is not equal to - s

ans is c

because we need b otherwise we cant cancel 0 on both sides

@ mods..i just could not see the question before 10:03..i tried refreshing but it was linking to question number 3 !

(1) qr + qs = r + s <=> q (r+s) = (r+s) <=> r + s = 0 or q = 1
Can't determine q -> not sufficient
(2) r is different to -s => r+s <> 0 . No information about q -> not sufficient

(1) + (2): r+s <> 0 & q(r+s) = (r+s) => q =1
Sufficient

My answer is C

The answer is: ( C)
Solution:
What is the value of integer ?

We have: (1) qr+qs = r+s
Then q(r+s) = r+s => (q-1)(r+s)=0 => q=1 or r=-s. So it’s not Sufficient
Together with (2) r≠-s, we have q=1.So the answer is C

Ans is C.
stmt 1) qr + qs = r + s => q(r+s) = (r+s)
=> q=1 if (r+s) not equal to 0 OR q does not have unique value if (r+s)=0
stmt 2) r not equal to -s => (r+s) not equal to 0
Hence, to find unique value of q stmt 1) & 2) both necessary

I will choose Answer C:

Statement 1:
qr + qs = r + s
q(r + s) = r + s

most of the people prefer to divide both sides by (r + S) and hence conclude that q = 1. As per my understanding, GMAT does not prefer that way because it eliminates one solution. (if one does as this, one will miss (r + s) = 0 as answer)

As per my understanding,
q(r + s) = r + s
q(r + s) - (r + s) = 0
(r + s)(q - 1) = 0

either (r + s) = 0 or (q - 1) = 0. if (r + s) = 0 then q can have any value.
statement 1 insufficient.

Statement 2:
r is not equal to -s does not provide any information about value of q
statement 2 is insufficient.

statement 1 and 2:
from statement 1, we know that either (r + s) = 0 or (q - 1) = 0
but from statement 2, we know that r NE -s, so (r + s) NE 0

substitute this in statemet 1. we will get (q - 1) = 0

q = 1

sufficient

OA please?

Ans : C
R+c should not be 0 in the 1st equation to get a value for Q
This is confirmed by 2nd statement. " R+c not= 0"
We need both statements together so ans is C

C.
- (2) is not sufficient since irrelevant. BD out
- (1) q (r+s) = r + s
(q-1)(r+s)= 0
=> Either (q-1) = 0 or (r+s) = 0. Not sufficient in case of (r+s) = 0. A out
- Both (1)&(2), from (2) we have r+s <>0, combine with (1) we have q = 1: sufficient

C
a - if r+s = 0; q could be anything
B - not sufficient
C- works. Q=1

why not (A)?
(i)q(r+s)=(r+s)
q=? ...(doesn't matter what r or s is , we have to find the q ;not to check whether is positive negative or zero);the value cant be found out insufficient so (A) is
sufficient
(ii) lacks info-insufficient

1) qr + qs = r + s thus, q (r+s) = (r+s). Now you can't divide since r+s=0. If r+s is not 0, then q=1. Hence insufficient
2) r+s is not = 0. no information about q.

Both combined - we can say that q = 1.
Thus, answer is C

A will only be the answer if statement (1) is sufficient to provide one exact answer to the question, what is the value of q?

A.

q(R+S) =(R+S)

Let the value of r and s be anything q will always be equal to 1.

Not correct approach.
what if R=S=0 then?
Q(R+S) = 1*(R+S) => Q=1 ?
as well as Q(R+S)=10*(R+S) =>Q=10 ?
and it can be shown to be true for any other number... So first you can not claim Q=1 this way.
Second, the conclusion u reached
Q(R+S) =(R+S) => Q=1
this is arrived when you've divided both sides by (R+S). Which can not be done if R+S = 0, as it will be illegal operation to divide by 0. Unless you are certain about r+s <>0, you can not reach to conclusion.

Dear vips - if r or s is 0... the equation will be 0 on both side..and u can not get the value of q.

if either r or s is 0 u still get q=1
isnt it?

Also if we are to consider this as an unanswerable case - then even point 2 wont help. r not equal to -s...could well mean r =s =0 again no answer and then reach the conclusion to be E.

What do you say?

Ans:C
Statement1:given qr+qs=r+s
=>q(r+s)=r+s
=>q=1 only when r not equal to -s
If r=-s,then q is undefined
Hence Statement1 is insufficient
Statement2:given r not equal to -s
No information about q
Hence Statement2 is insufficient

By combining both statements 1 and 2
q=1 when r not equal to -s
Hence C is the correct answer